*Here is the link for Rdata file, incase if you need*: https://drive.google.com/drive/folders/1H_EfjMUd6ehOqhZ43DtHp51Gz7_yg_8-?usp=sharing

Question 3 (9 Marks): use of a software is not recommended

The multivariate observations of 4 variables were obtained for 20 subjects and these observations were denoted by $1, . .., 120, where each r; is a 4 X 1 vector containing 4 values from the 4 variables. Let the population mean vector be A = (M1, /2, #3, #) . Suppose we wish to test the following hypotheses involving different contrasts: Ho : p1 - atest = 0. 10 - Bitesti = 0, 3 3 3 = 0. Let the significance level for the test be a = 5%. (a) (3 Marks) Explain how to test this hypothesis. In your answer you must include: (i) assumptions made, (ii) test statistic, and (iii) how to decide on rejecting or retaining the null hypothesis. (b) (3 Marks) Write down the T2 simultaneous confidence intervals for all contrasts.(c) (3 Marks) Write down the Bonferroni simultaneous confidence intervals for all contrasts